GIAN Course on

Population Balance Equations with Applications

26th - 30th November 2018

Venue: Indian Institute of Technology Roorkee, Roorkee-247667,Uttarakhand, India

Overview of the course

Engineers, natural scientists and, increasingly, researchers and practitioners working in economics and other social sciences, use mathematical modelling to solve problems arising in their disciplines. Mathematical modelling may lead to many mathematical objects describing the real world. However, most often, the laws of physics and, increasingly, also those of other sciences are expressed in terms of differential or integro-differential equations. If one models systems evolving with time, then the variable describing time plays a special role, as the equations are built by balancing the change of the system in time against its `state space behavior. Such equations are called evolution equations. There are two main types of conservative laws: those balancing the change of the numbers of interacting objects and those that balance the energy in the process. In these lectures we shall focus on equations of the first type. Here the modelling leads to the so-called kinetic models (similar to Master Equations in the theory of Markov processes), where one considers the loss and gain of objects at a particular state through motion in the physical state as well as through interactions, both with each other and with the environment. A prototype for such equations is the Boltzmann equation describing the dynamics rarefied gases, derived in the XIX century but the argument leading to that equation, over the years has been extended to a range of problems in epidemiology, genetics, learning, chemical engineering and in many other fields. During these lectures, we will introduce transport models and their generalizations, including network transport and McKendric population equation Smoluchowski — Muller fragmentation-coagulation processes, whose applications range from polymerisation processes of chemical engineering, through rock crushing and planetesimal formation, to algae dynamics and animal groupings, and we will discuss a selection of them. Models of that type are known to practitioners in science and engineering and many of them have well established explicit solutions (that will be mentioned in the course). However, in some case these solutions have properties that are pathological from the applications point of view.

Objectives of the course

The primary objectives of the course are as follows:

  • Exposing participants to the fundamentals of building kinetic type models in various areas of natural sciences and engineering ‐ in particular, the transport models, and the Smoluchowski ‐ Muller coagulation-fragmentation equation
  • Providing participants with tools for constructing explicit solutions to selected models and determining whether they are physical or unphysical.
  • Making the participants conversant with basic tools of functional analysis, dynamical systems theory and numerical analysis.
  • Exposing the participants to the methods of qualitative analysis of selected models with identification of pathological ranges of parameters and investigations of the break-down of well-posedness.
  • Discussion on convergence analysis of various numerical methods for solving population balance equations.
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Registration Fee for the Workshop

  • M.Sc/M.Phil Students: Rs. 1,500./-

  • M. Tech./ Ph.D. Student/ Post Doctoral: Rs. 2,500/-

  • Participants from acedemic/technical/R & D institution/industry: Rs. 5,000/-

  • Participants from abroad: $250

The above fee includes all instructional materials, computer use for tutorials and assignment and free internet facility. The participants will be provided with accommodation on payment basis. Hotel accommodation may also be arranged on payment basis at nearby places, if required.

(For the regestration at GIAN portal you have to pay Rs. 500 extra.)

Registration and Accommodation

Registration at GIAN portal

To attend the course, first register at the GIAN portal, where you have to pay Rs. 500 separately for life time. The web address for registration is:
Click here for registration at the GIAN portal (Please fill all the all details there, pay the registration fee and then click to register the course ''Population Balance Equations with Applications'' from the list of the courses.)

Registration for the Workshop:

After completing the registration at GIAN Portal, fill the following registration form Click here to fill the registration form
( The registration form is at the 4th page, download it and after filling the form, send the scanned copy to the Prof. A. K. Giri at the email ankikgiri.fma[at] )

Next, pay the registration fee for the workshop separately (as mentioned in the above box). For making e-payment, use the following link

Click here to pay the registration fee for the workshop

(NOTE-Do not forget to mention the conference code (GIAN-48-MAT) at the time of making the payment.)

Alternately, use the following Bank details for the payment.

Bank Name State Bank of India
Branch Name IIT Roorkee
Institution Account Name Confrence, Seminar and Symposium, IIT Roorkee
Account no. 33136732957
IFSC Code SBIN0001096
Complete Branch Adress IIT Roorkee-247667
MICR No. 247002094
Account Type Savings

(Do not forget to mention the conference code (GIAN-48-MAT) at the time of making the payment.)


After making the payment, it is mandatory to send the payment receipt to the email address ankikgiri.fma[at]


The participants may be provided with hostel accommodation, depending on availability, on payment basis.

The outstation participants who require accommodation should send a request to ankikgiri.fma[at] with the subject ''Request for Accommodation''.

The participants who requested accommodation should fill up the following application form and send (the scanned copy)their request to ankikgiri.fma[at]
up to October 5, 2018. For any query do not hesitate to contact Prof. Ankik Kumar Giri (address is given below with mobile no.).


Foreign Expert(Prof. J. Banasiak)

Prof. J. Banasiak is a Professor at University of Pretoria from January 2015. He is also serving as DST/NRF SARCHI Chair in Mathematical Models and Methods in Biosciences and Bioengineering. He obtained his MSc (Engineering) from the Technical University of Lodz in 1981 and PhD from the Strathclyde University in Glasgow in 1989 on elliptic and parabolic problems in irregular domains. Later, his Habilitation (DSc) conferred by the University of Warsaw in 1999 and the State title of Professor conferred by the President of the Republic of Poland in 2007. In 1992, he joined the Department of Mathematics and Applied Mathematics at the University of Natal and was there as a Senior Professor since 2008 — 2015 and a Research Professor 2011 — 2015. Prof. Banasiak has authored/co-authored 5 research monographs including: Methods of Small Parameter in Mathematical Biology, Birkhauser, 2014, (with M. Lachowicz), Difference and Differential Equations in Mathematical Modelling, Cambridge University Press, 2013, Perturbations of positive semigroups with applications, Springer, 2006, (with L. Arlotti), and Singularly Perturbed Evolution Equations with Application to Kinetic Theory, World Scientific, 1995 (with J.R. Mika). He has published over 100 refereed research papers. He is also a Visiting Professor at the University of Strathclyde, UK since 2010. Fields of interest: Functional analysis and semigroup theory with applications to models in natural and physical sciences, dynamical systems, asymptotic analysis and methods of small parameter, network dynamics.

Research interests: Nonlocal integro-differential models in kinetic theory, mathematical biology and fragmentation-coagulation theory, asymptotic analysis of multiple scale problems, asymptotics of dynamical systems of networks, structured population dynamics.
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Indian Expert (Prof. Ankik Giri)

Prof. Ankik Giri is an Assistant Professor in Mathematics at IIT Roorkee, Roorkee, India since June 2014. He received his PhD in Mathematics from International Max-Planck Research School at Ottovon-Guericke University, Magdeburg, Germany in 2010. After completing his PhD, he worked as a Postdoctoral Fellow at Montan University Leoben, Austria since 2010-2012. Later, he served as a Research Scientist at Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria since 2012-2014. He has authored one monograph on Mathematical and Numerical Analysis for Coagulation-Fragmentation Equations in 2011. Dr. Giri has published several research papers in the international refereed journals.

Research interests: Partial-integro differential equations, Coagulation and fragmentation processes, Stochastic PDEs and regularization theory for Inverse problems.
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Contact Details

Visit us at:
Prof. Ankik Kumar Giri
Department of Mathematics
Indian Institute of Technology Roorkee, Roorkee
Uttrakhand, India- 247667
Tel: +91 1332 284818
Mobile no: +91 8439188828
Email at ankikgiri.fma[at]
Clik here for the web address